Method of making film resistors



March 19, 1968 I s.` M. cox 3,373,486

METHOD OF MAKING FILM RESISTORS Filed Dec. 2, 1965 Sheets-Sheet. l

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March 19, 1968 s. M. COX 3,373,486

METHOD OF MAKING FILM RESISTORS Filed Deo. 2, 1965 5 Sheets-Sheet 5 United States Patent Office 3,373,486 Patented Mar. 19, 1968 3,373,486 METHOD OF MAKING FILM RESISTORS Shaun Maturn Cox, South Shields, England, assignor to National Research Development Corporation, London, England Filed Dec. 2, 1963, Ser. No. 327,244 Claims priority, application Great Britain, Dec. 7, 1962, 46,259/ 62 4 Claims. (Cl. 29--610) This invention relates to film resistors and has reference to film resistors of the metallic oxide type.

A film resistor of the metallic oxide type is conveniently made up as a thin film of a metallic oxide, e.g. tin oxide with a small admixture of antimony oxide, 'deposited upon a glass substrate. The substrate may be plane or curved e.g. the outside surface of a glass rod or tube or the inside surface of a glass tube.

Resistors of this type are of high quality and well suited for use for electronic purposes; resistors having very small temperature co-eiiicients are possible.

A ditiiculty which is encountered in connection with these resistors is that theyare prepared at relatively high temperature and when they are cooled to whatever operating temperature they are intended for instability becomes apparent.

According to the invention therefore a method of stabilising a resistor of the thin film type comprises, raising a film resistor on its substrates to an enhanced temperature whilst simultaneously establishing a vapour pressure of a polar liquid which at the enhanced temperature enables rapid stabilisation of the resistor to take place to the value desired at the temperature of operation of the resistor, and then cooling and `drying the resistor concurrently after stabilisation until its operating temperature is reached.

The polar liquid may conveniently be water.

In order to make the invention clearer the principles involved will be discussed and an example of a method according to the invention will be described reference being made to the accompanying drawings, in which:

FIG. 1 shows diagrammatically in cross-section an oven in which steps of the method are carried out;

FIG. 2 shows a graph of relaxation time against temperature for a typical resistor substrate glass;

FIG. 3 shows a typical graph used in choosing the conditions of the method of the example.

It has become clear from our Work on tin-antimony oxide film resistors on glass substrates that instability occurs owing to interactions of the barrier-layer type between the oxide layer and the glass substrate; we have noted that ion mobilities increase as the temperature is reduced and delay in achieving stability now appears to be understandable in terms of mobility of ions in the substrate.

It appears reasonable to assume therefore that the behaviour of the unstable resistor can be demonstrated by a model in which -a variable unstable resistive element is shunted across a stable resistive lm. This model is also convenient because the same variable element can be assumed to apply for all similar resistors whatever their film thickness. p

Work has also been done to investigate instability, iLe. the manner in which resistance value changes with time.

Supposing that the time delayed effects are entirely confined to the interface resistance s we have for a change in resistance AR, where 1/R=x/r+1/s, r being the bulk resistivity of a film of thickness x,

@eine R l-RFU) where F(t) denotes some function of time. Limiting consideration to cases where AR/ R is small we have approximately in which we have now to establish the form of the function F(t).

It has been shown experimentally that the empirical relation, resistance proportional to square root of time, represents the initial stages of drift `at low temperature. At high temperatures there is a definite terminal value so that this is clearly only an approximation. The mechanism of the change proves to depend on diffusion of ions in the glass substrate under the influence of space charge at the interface and therefore it is natural to look for an appropriate diffusion law or the mathematically identical expression for heat conduction to express FU).

If we suppose the electrical conductivity of the interface is proportional to say the depth of a depletion layer and that this in turn is proportional to the ion concentration at the glass surface the appropriate analogue is the surface temperature v of a semi-infinite solid initially at temperature V radiation into a medium at zero temperature.

According to Carslaw and Jaeger, Conduction of Heat, Oxford 1959,

where x is proportional to t/a and erfc. denotes an error function relation, namely erfc.x=j2; im 1:*52635 For our case We write x2=t/w and define w as a relaxation time inversely proportional to the mobility of the ions in the glass and therefore proportional to the electrical resistivity of the glass. Writing also y for AR/R2 and Y for the terminal value of AR/R2 y=Y(1-ex2erfc.a:) where x is small this reduces to This relation has been found to express the resist-ance variations over a range of temperatures corresponding to a range of relaxation times from a few minutes to over 1,000 hours. The values of w for `a typical glass C46 glass (made by A.E.I. Lamp & Lighting Co. Ltd.) are given in FIG. 2 plotted `against the reciprocal of the Absolute temperature. It is interesting to note that the activation energy is in fact the saine as that for electrical resistivity for this glass-manufacturers figures for which are also plotted.

Study of resistor behavior at around 300 C. where response to change is fairly rapid, suggests that we can infer the behavior on the principle that the changes are superposable. The mechanism involved is presumably identical to that involved in the anomalous charging and discharging currents in glass dielectrics where such a principle applies.

Mathematically we can express the principle in terms of the heat conduction analogue of the last section, supposing that the medium into which the solid is radiating is at a temperature (V-a) from T to 0, and at temperature (V-b) from 0 to t. In our case these limiting ternperatures are identified with the terminal values Y and Y" which the resistance would attain if given suicient time. The resistance at any (positive) time is then given by y: Y' (.Y" r'wzerfw- Y'e-Zerfaz where x2=t/w and z2: (t-T)/w This principle of superposition is of particular significance in view of the extremely rapid variation of the terms in the expression at short times. As a consequence the immediate response of the resistor to a change is largely independent of its previous history and a resistor which is far removed from its stable value will respond to a recent change in a direction which may be contrary to its long term trend. On the other hand after long times it is the magnitude of the earlier event which dictates its prominence.

Consider a resistor of zero instantaneous coeicient and suppose it is taken from 20 to 120 and held for one hour before measurement is made. The resistor is unlikely to be stabilised to either of these temperatures however; the trend towards stabilisation in one hour will not be significant. Nevertheless the act of taking the resistor from 20 to 120 has, by the principle of superposition, induced a change corresponding to the difference in stabilised value at 120 and 20. For a resistor of 300 ohms per square on C46 glass this difference can be obtained (23%) by extrapolation in FIG. 3. The relaxation times for this glass are 2.5 1011 and 4 105 hours at the respective temperatures (FIG. 2).

Using the expression y=2Y(t/1rw)/ we have on heating AR/Ri=4.l4 l04 and on cooling after one hour AR/R= 5.2 7 approximately, i.e. there is a detectable increase on heating which is not recovered on cooling.

It is interesting to note that if the heating is now repeated there is only a small additional gain because the act of coolingalthough it scarcely affects the resistance-is remembered and by superposition cancels the effect of the second heating.

Such seemingly puzzling features of resistance behaviour can be predicted with accuracy if in the calculations one always measures time in terms of the relaxation time appropriate to the particular temperatures. Taking the instance just cited as an example, when the resistor is heated twice from a temperature at which wi=w to one at which w=w, the change in resistance at low temperatures may be shown to be given by 7 r1 /.7 J=(/wll 1/2 (Tl/w/ /wl/)1/Z r"/w"+T'/w'+f/w" 1f2 where t is measured from the start of the second heat and T" and T are the times spent previously `at the upper and lower temperatures.

It can be demonstrated that there is a terminal value of resistance to which the resistance tends at each temperature.

In a further experiment the resistive ilrn is formed in 'the bore of a 3 mm. glass tube and spira'lled to a convenient value. The `film can therefore be hermetically :sealed or a stream of dry or humid air passed over it. The lcompleted resistor with a control thermocouple is placed in a small furnace of very low thermal capacity so that changes in temperature can be rapid. The circulating air is passed either through temperature controlled water or through silica gel and P205 drying columns. The resistance is recorded continuously as AR/R by a recorder arranged as a Wheatstone bridge.

The results when automatically plotted on a linear time scale have a `deceptive appearance in that the drift rate has slowed down so much by the time r=w that it appears to indicate an end point. However when the results are tted by the error function y: Y( l eX2 erfax) the relaxation times may be determined and the terminal values establishedthus presenting the information contained in FIG. 2 and FIG. 3, which together provide the data necessary for the exercise of the stabilising process described below. We have discovered that the expression has equal validity whether applied to resistance changes resulting from temperature change or to changes in humidity.

The stabilised resistance value of a resistor is substantially a linear function of temperature between 150 and 350 C., although the accuracy of the extrapolated values is not great enough to exclude a 1/TA relationship. Above 350 there appears to be a maximum but results at this temperature are not always reproducible and are no doubt influenced by deep-seated irregularities of ion distribution in the glass and possibly influenced by diffusion of silver in the contacts. It is convenient to assume a simple linear relation between terminal value and temperature since from a practical point of view errors are more likely to arise owing to the very rapid variation of relaxation time with temperature.

It will be seen from FIG. 3 that the terminal value of resistance is very sensitive to the humidity of the ambient air. A 10 change in dew point is as effective as a 40 change in temperature. The relaxation time however depends only on the temperature and most of the points in FIG. 2 are obtained by alternating between wet and dry to induce easy-to-follow trends.

The results obtained suggest, that the lowering of the terminal value is proportional to p where p is the partial pressure of water vapour, water being the wetting agent used. In plotting the results however the graph of FIG. 3 has been scaled in terms of dew point for ready practical application.

A method of predetermining the stability of a thin ilm tin-antimony oxide resistor on a glass substrate has been developed from our work described above and will now be described as applied on a small scale to a single resistor.

A typical controlled environment wherein the method of the present invention may be practiced is shown in FIG. 1 where an oven 1 heated by an electric winding 2 is mounted in an insulating outer case 3. The bottom of the oven 1 is supported on pillars 4, only two of which are shown, and leads 5 connect a current supply to the winding 2.

A thin film resistor comprising a tin-antimony oxide layer 6 mounted on a glass (A.E.I. Lamp & Lighting Co. Ltd.s C46 glass) substrate 7 is located within the oven 1 in close proximity to a thermocouple 8. Leads 9 are attached to the resistor for monitoring purposes and lead out through a grommet in the top closure plate 10 of the oven 1 and through the lid 11 of the outer case 3. Leads 12 are attached to the thermocouple 8 and lead out through the plate 10 and the lid 11. It will be appreciated that for purposes of illustration the relative dimensions of the apparatus and the resistor have had to be changed particularly those of the resistor layer 6 and its substrate 7. Typically the substrate 7 would be 3x10-2 in. thick and the layer 2.4 10-6 in. thick.

An inlet pipe 13 and an outlet pipe 14 are provided to enable the atmosphere in the oven l to be controlled. The pipe 13 is conveniently connected to a source of air (not shown) which includes means for drying or wetting the air to give known humidity values.

In carrying out the method the temperature of the oven 1 is raised so that the resistive iilm 6 and substrate 7 are subjected to a predetermined high temperature the humidity also being raised. The temperature and humidity are so selected by reference to a set of curves as shown in FIG. 3 that the resistor stabilises rapidly, typically achieving completion after 10 hours at the high temperature and the high humidity, to the resistance value of the dry resistor at a required operating temperature.

After the resistor has stabilised--and this will be indicated by reading its resistance from a recorder connected to the monitoring leads 4-the temperature of the oven 1 and the humidity of the air incoming at the pipe 13 are reduced until the resistor is brought to its dry state at its predetermined operating temperature. The auxiliary apparatus for the control of temperature and humidity being conventional there is no need to describe its detailed operation here. It may be worthy of note however that the humidity and indeed the temperature are reduced concurrently, in suitable steps or continuously as con- Venient. The required action depends upon the realisation from our work that resistance Value responds to humidity changes in a manner similar to that in which it responds to temperature changes, only in the reverse sense,

In a typical example involving a tin-antimony oxide layer of 200 ohms per square on a C42 glass substrate the resistor was stabilised for 8 hours at a temperature of 350 C. in air of 40 C. dew point and then without change in humidity for 1 hour at a temperature of 290 C. before being simultaneously dried and brought to its predetermined operating temperature of 150 C. Stability figures were obtained as follows:

It will be appreciated from the foregoing that even by heat treatment alone, of resistors after deposition, it is possible to improve their stability. The final instability value is approximately proportional to the temperature difference between the operating condition and the final treatment temperature; as low a final temperature as possible is therefore achieved as quickly as possible. Moreover reductions in time are possible by using several stages although this might be at some cost in the long term stability of the resistor. However such residual instabilities can be calculated by the formula disclosed above and in practice it is found that it is unnecessary to achieve complete stabilisation at the higher temperatures but only to reduce the residual instability to a tolerable value.

It will be seen however that a much greater improvement is obtained by the method described in which control of humidity and temperature is employed. The conditions chosen vary with substrate material and possibly with the value and type of film resistor layer. It may be necessary then to undertake further simple experiments where diierent substrate material for example, is involved to obtain curves corresponding to those of FIG. 3 and particularly that of FIG. 2, for use in the design of an appropriate stabilisation treatment. These experiments however do not go beyond what those skilled in the art can accomplish and, where the stability required is within the capacity of a given substrate, it is always possible to choose a satisfactory treatment.

For most examples involving glass substrate materials adequate method design curves of the kind shown in FIG. 3 or FIG. 2 for the C46 glass material can be obtained from experiments in which two temperatures and two humidities are chosen and the resistance variations for changes between these parameters are determined by the experiment described. Estimates of stabilisation times can also be made to enable comparisons to be made between possible arrangements of the method.

Although the example of the method described and the curves of FIG. 2 refer only to relatively low humidity values, high values are possible if shorter stabilisation times are sought.

A form of resistor to which the method can be applied very conveniently is that in which a metallic oxide film is deposited on the inside of a glass tube substrate. This form of resistor enables the humidity conditions to be determined precisely by means of gas flow through the tube.

In the example described humidity has been controlled by adjustment of water vapour content. The effect of changing the humidity is to change the dielectric constant at the resistor substrate/oxide layer interface. Consequently if convenient, the vapour of polar liquids, other than water, having a high dielectric constant may be used.

I claim:

1. A method of stabilizing a resistor of the thin film type comprising: choosing a stabilizing temperature sufficiently high to allow rapid stabilization of resistance and a stabilizing vapour pressure of a polar liquid such that the terminal value of resistance to which the resistor is stabilized at the said stabilizing temperature and the said stabilizing vapour pressure is the value desired at the desired temperature of operation of the resistor, in a controlled environment raising the resistor on its substrate to the said stibilizing temperature while simultaneously establishing the said stabilizing vapour pressure, maintaining the said stabilizing temperature and the said stabilizing vapour pressure for a suicient length of time for the resistance of the resistor to be stabilized to the extent desired and then cooling and drying the resistor concurrently after stabilization by concurrently reducing the temperature and the vapour pressure of the controlled environment until the said desired temperature of operation of the resistor is reached whereby the stabilized resistance of the resistor is maintained.

2. A method of stabilising a resistor as claimed in claim 1 and in which the polar liquid is water.

3. A method of stabilising a resistor as claimed in claim 1 and in which the substrate comprises a glass tube and the thin film is deposited on the inside of the glass tube.

4. A method of stabilising a resistor as claimed in claim 2 and in which the substrate comprises a glass tube and the thin film is deposited on the inside of the glass tube.

References Cited UNITED STATES PATENTS 2,877,330 3/1959 Kelm 338-258 2,994,847 8/1961 Vodar 117--47 X 3,108,019 10/1963 Davis 117-211 X 3,324,706 6/ 1967 Russell 266-5 X JOHN F. CAMPBELL, Primary Examiner.

I. CLINE, Assistant Examiner. 

1. A METHOD OF STABILIZING A RESISTOR OF THE THIN FILM TYPE COMPRISING: CHOOSING A STABILIZING TEMPERATURE SUFFICIENTLY HIGH TO ALLOW RAPID STABILIZATION OF RESISTANCE AND A STABILIZING VAPOUR PRESSURE OF A POLAR LIQUID SUCH THAT THE TERMINAL VALUE OF RESISTANCE TO WHICH THE RESISTOR IS STABILIZED AT THE SAID STABILIZING TEMPERATURE AND THE SAID STABILIZING VAPOUR PRESSURE IS THE VALUE DESIRED AT THE DESIRED TEMPERATURE OF OPERATION OF THE RESISTOR, IN A CONTROLLED ENVIRONMENT RAISING THE RESISTOR ON ITS SUBSTRATE TO THE SAID STIBILIZING TEMPERATURE WHILE SIMULTANEOUSLY ESTABLISHING THE SAID STABILIZING VAPOUR PRESSURE, MAINTAINING THE SAID STABILIZING TEMPERATURE AND THE SAID STABILIZING VAPOUR PRESSURE FOR A SUFFICIENT LENGTH OF TIME FOR THE RESISTANCE OF THE RESISTOR TO BE STABILIZED TO THE EXTENT DESIRED AND THEN COOLING AND DRYING THE RESISTOR CONCURRENTLY AFTER STABILIZATION BY CONCURRENTLY REDUCING THE TEMPERATURE AND THE VAPOUR PRESSURE OF THE CONTROLLED ENVIRONMENT UNTIL THE SAID DESIRED TEMPERATURE OF OPERATION OF THE RESISTOR IS REACHED WHEREBY THE STABILIZED RESISTANCE OF THE RESISTOR IS MAINTAINED. 